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Math Help - Solve 2

  1. #1
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    Solve 2

    Same as other one. How would I solve derivative simplifying results?

    g(x)=√2x^4+x^2+1

    r(x) 2x^2-5x^-12/x-4

    m(x) = -5(x^4+3)^8

    k(x)=2x/x^2+2
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  2. #2
    MHF Contributor
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    For g(x), I'm taking that to be \sqrt{2x^4+x^2+1} Let u = 2x^4+x^2+1 and let \frac{du}{dx}=8x^3+2x So g(x) can now be written as \sqrt{u} Now taking the derivative, you get g'(x)=\frac{1}{2\sqrt{u}}*\frac{du}{dx}. Now back substitute everything in. Does this method make sense? It can be a lot to take in.

    For r(x) and k(x), just use the quotient rule.

    \frac{d}{dx}\frac{u}{v}=\frac{vu'-uv'}{v^2}

    All of the questions use the powerful CHAIN RULE. Make sure to learn that solidly.
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